Solve x-1/4leq2x-3/3

$$\frac { x - 1 } { 4 } \leq \frac { 2 x - 3 } { 3 }$$

Solve for x

$$x\geq \frac{9}{5}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\left(x-1\right)\leq 4\left(2x-3\right)$$

Use the distributive property to multiply 3 by x-1.

$$3x-3\leq 4\left(2x-3\right)$$

Use the distributive property to multiply 4 by 2x-3.

$$3x-3\leq 8x-12$$

Subtract 8x from both sides.

$$3x-3-8x\leq -12$$

Combine 3x and -8x to get -5x.

$$-5x-3\leq -12$$

Add 3 to both sides.

$$-5x\leq -12+3$$

Add -12 and 3 to get -9.

$$-5x\leq -9$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{-9}{-5}$$

Fraction \frac{-9}{-5} can be simplified to \frac{9}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{9}{5}$$